Low-symmetry two-dimensional ${\mathrm{BNP}}_2$ and $C_2\mathrm{SiS}$ structures with high and anisotropic carrier mobilities

We study the stability and electronic structure of previously unexplored two-dimensional (2D) ternary compounds ${\mathrm{BNP}}_2$ and ${\mathrm{C}}_2\mathrm{SiS}$. Using ab initio density functional theory, we have identified four stable allotropes of each ternary compound and confirmed their stability by calculated phonon spectra and molecular dynamics simulations. Whereas all ${\mathrm{BNP}}_2$ allotropes are semiconducting, we find ${\mathrm{C}}_2\mathrm{SiS}$, depending on the allotrope, to be semiconducting or semimetallic. The fundamental band gaps of the semiconducting allotropes we study range from $1.4\mathrm{eV}$ to $2.2\mathrm{eV}$ at the HSE06 level and display carrier mobilities as high as $1.5\times {10}^5{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$. Such high mobilities are quite uncommon in semiconductors with so wide band gaps. Structural ridges in the geometry of all allotropes cause a high anisotropy in their mechanical and transport properties, promising a wide range of applications in electronics and optoelectronics.

Figure 1

Ball-and-stick models of relaxed monolayer structures of (a) ${\alpha }_1$, (b) ${\beta }_1$, (c) ${\alpha }_2$ and (d) ${\beta }_2$ allotropes of ${\mathrm{BNP}}_2$, and (e) ${\alpha }_1$, (f) ${\beta }_1$, (g) ${\alpha }_2$ and (h) ${\beta }_2$ allotropes of ${\mathrm{C}}_2\mathrm{SiS}$ in top and side view. The lattice vectors are indicated by red arrows.

Figure 2

Effect of uniaxial in-layer strain on the relative binding energy $\mathrm{\Delta }E$ in monolayers of (a) ${\mathrm{BNP}}_2$ and (b) ${\mathrm{C}}_2\mathrm{SiS}$. Results for different allotropes are distinguished by color and symbols. Results for strain along the $x$ direction are shown by solid lines and for strain along the $y$ direction by dashed lines.

Figure 3

Electronic structure of a ${\mathrm{BNP}}_2$ monolayer. Shown are the calculated band structure $E\left(\mathbf{k}\right)$ and the density of states (DOS) including its projection on individual atoms (left panels), the partial charge density distributions at the valence band maximum (VBM), and the conduction band minimum (CBM) (right panels) of the (a) ${\alpha }_1$, (b) ${\alpha }_2$, (c) ${\beta }_1$, and (d) ${\beta }_2$ allotropes. All results are based on the DFT-PBE functional with the exception of DFT-HSE06 data, which are shown by the red dashed lines in the band structure plots. The blue arrows indicate the fundamental band gap. Contributions of different atoms are distinguished by color in the PDOS plots. Isosurface plots of the partial charge density are presented at the isosurface value of $8.0\times {10}^{-3}$ e/${\mathrm{Bohr}}^3$ for all allotropes.

Figure 4

Contour plots of the energy dispersion $E$(k) of the top valence band (left panels) and the lowest conduction band (right panels) in (a) ${\alpha }_2\text{−}{\mathrm{BNP}}_2$ and (b) ${\beta }_2\text{−}{\mathrm{BNP}}_2$. The Fermi level is set as the reference energy of zero.

Figure 5

Electronic structure of a ${\mathrm{C}}_2\mathrm{SiS}$ monolayer. The calculated band structure $E\left(\mathbf{k}\right)$ and the density of states (DOS) including its projection on individual atoms are shown in the left panels. The partial charge density distributions at the valence band maximum (VBM) and the conduction band minimum (CBM) for the semiconducting allotropes and for the frontier states in the semimetallic allotropes are shown in the right panels. Results are presented for the (a) ${\alpha }_1$, (b) ${\alpha }_2$, (c) ${\beta }_1$, and (d) ${\beta }_2$ allotropes. All results are based on the DFT-PBE functional with the exception of DFT-HSE06 data, which are shown by the red dashed lines in the band structure plots. The blue arrows indicate the fundamental band gap in the semiconducting allotropes. Contributions of different atoms are distinguished by color in the PDOS plots. Isosurface plots of the partial charge density are presented at the isosurface value of $8.0\times {10}^{-3}\mathrm{e}/{\mathrm{Bohr}}^3$ for all allotropes.

Figure 6

Band dispersion in the semimetallic allotropes ${\alpha }_2\text{−}{\mathrm{C}}_2\mathrm{SiS}$ (left) and ${\beta }_2\text{−}{\mathrm{C}}_2\mathrm{SiS}$ (right) near the Fermi level. $E($k) results are presented as 3D plots in (a),(b) and 2D contour plots in (c),(d). The energy with respect to $E_F=0$ is represented by color.

Figure 7

Ball-and-stick model of metastable structures related to the ${\alpha }_1$ and ${\beta }_1$ allotropes of ${\mathrm{BNP}}_2$, shown in top view. Cohesive energies $E_{\text{coh}}$ are presented below each structure, with the value for the most stable configuration highlighted in red.

Figure 8

Ball-and-stick model of metastable structures related to the ${\alpha }_1$ and ${\beta }_1$ allotropes of ${\mathrm{C}}_2\mathrm{SiS}$, shown in top view. Cohesive energies $E_{\text{coh}}$ are presented below each structure, with the value for the most stable configuration highlighted in red.

Figure 9

Ball-and-stick model of metastable structures related to the ${\alpha }_2$ and ${\beta }_2$ allotropes of ${\mathrm{BNP}}_2$, shown in top view. Cohesive energies $E_{\text{coh}}$ are presented below each structure, with the value for the most stable configuration highlighted in red.

Figure 10

Phonon spectra for monolayers of (a) ${\alpha }_1\text{−}{\mathrm{BNP}}_2$, (b) ${\beta }_1\text{−}{\mathrm{BNP}}_2$, (c) ${\alpha }_2\text{−}{\mathrm{BNP}}_2$, (d) ${\beta }_2\text{−}{\mathrm{BNP}}_2$, (e) ${\alpha }_1\text{−}{\mathrm{C}}_2\mathrm{SiS}$, (f) ${\beta }_1\text{−}{\mathrm{C}}_2\mathrm{SiS}$, (g) ${\alpha }_2\text{−}{\mathrm{C}}_2\mathrm{SiS}$, and (h) ${\beta }_2\text{−}{\mathrm{C}}_2\mathrm{SiS}$.

Figure 11

Fluctuations of the total potential energy (left panels) and structural snap shots after 15 ps (right panels) for (a) ${\alpha }_1\text{−}{\mathrm{BNP}}_2$, (b) ${\alpha }_2\text{−}{\mathrm{BNP}}_2$, (c) ${\beta }_1\text{−}{\mathrm{BNP}}_2$, and (d) ${\beta }_2\text{−}{\mathrm{BNP}}_2$ monolayers during canonical MD simulations at $300\mathrm{K}$, $500\mathrm{K}$, and $1000\mathrm{K}$.

Figure 12

Fluctuations of the total potential energy (left panels) and structural snap shots after 15 ps (right panels) for (a) ${\alpha }_1\text{−}{\mathrm{C}}_2\mathrm{SiS}$, (b) ${\alpha }_2\text{−}{\mathrm{C}}_2\mathrm{SiS}$, (c) ${\beta }_1\text{−}{\mathrm{C}}_2\mathrm{SiS}$, and (d) ${\beta }_2\text{−}{\mathrm{C}}_2\mathrm{SiS}$ monolayers during canonical MD simulations at $300\mathrm{K}$, $500\mathrm{K}$, and $1000\mathrm{K}$.

Figure 13

Carrier mobility versus band gap for different 2D materials. Results for semiconducting allotropes predicted in this study, shown by the red symbols, are compared to previously reported results, cited in the text and shown by the black symbols. All results have been obtained at the PBE level of DFT.